Bayesian analysis improves experimental studies about temporal patterning of aggression in fish

This study aims to describe a Bayesian Hierarchical Linear Model (HLM) approach for longitudinal designs in fish's experimental aggressive behavior studies as an alternative to classical methods In particular, we discuss the advantages of Bayesian analysis in dealing with combined variables, non-statistically significant results and required sample size using an experiment of angelfish (Pterophyllum scalare) species as case study. Groups of 3 individuals were subjected to daily observations recorded for 10 min during 5 days. The frequencies of attacks, displays and the total attacks (attacks + displays) of each record were modeled using Monte Carlo Markov chains. In addition, a Bayesian HLM was performed for measuring the rate of increase/decrease of the aggressive behavior during the time and to assess the probability of difference among days. Results highlighted that using the combined variable of total attacks could lead to biased conclusions as displays and attacks showed an opposite pattern in the experiment. Moreover, depending of the study, this difference in pattern can happen more clearly or more subtly. Subtle changes cannot be detected when p-values are implemented. On the contrary, Bayesian methods provide a clear description of the changes even when patterns are subtle. Additionally, results showed that the number of replicates (15 or 11) invariant the study conclusions as well that using a small sample size could be more evident within the overlapping days, that includes the social rank stability. Therefore, Bayesian analysis seems to be a richer and an adequate statistical approach for fish's aggressive behavior longitudinal designs.